larrj(3)

NAME
larrj - larrj: step in stemr, refine eigval estimates

SYNOPSIS

  Functions
subroutine dlarrj (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info)
DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.
subroutine slarrj (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info)
SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

Detailed Description

Function Documentation

  subroutine dlarrj (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e2, integer ifirst, integer ilast, double precision rtol, integer offset, double precision, dimension( * ) w, double precision, dimension( * ) werr, double precision, dimension( * ) work, integer, dimension( * ) iwork, double precision pivmin, double precision spdiam, integer info)

DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

Purpose:

    !>
    !> Given the initial eigenvalue approximations of T, DLARRJ
    !> does  bisection to refine the eigenvalues of T,
    !> W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial
    !> guesses for these eigenvalues are input in W, the corresponding estimate
    !> of the error in these guesses in WERR. During bisection, intervals
    !> [left, right] are maintained by storing their mid-points and
    !> semi-widths in the arrays W and WERR respectively.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (N)
    !>          The N diagonal elements of T.
    !>

    E2

    !>          E2 is DOUBLE PRECISION array, dimension (N-1)
    !>          The Squares of the (N-1) subdiagonal elements of T.
    !>

    IFIRST

    !>          IFIRST is INTEGER
    !>          The index of the first eigenvalue to be computed.
    !>

    ILAST

    !>          ILAST is INTEGER
    !>          The index of the last eigenvalue to be computed.
    !>

    RTOL

    !>          RTOL is DOUBLE PRECISION
    !>          Tolerance for the convergence of the bisection intervals.
    !>          An interval [LEFT,RIGHT] has converged if
    !>          RIGHT-LEFT < RTOL*MAX(|LEFT|,|RIGHT|).
    !>

    OFFSET

    !>          OFFSET is INTEGER
    !>          Offset for the arrays W and WERR, i.e., the IFIRST-OFFSET
    !>          through ILAST-OFFSET elements of these arrays are to be used.
    !>

    W

    !>          W is DOUBLE PRECISION array, dimension (N)
    !>          On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
    !>          estimates of the eigenvalues of L D L^T indexed IFIRST through
    !>          ILAST.
    !>          On output, these estimates are refined.
    !>

    WERR

    !>          WERR is DOUBLE PRECISION array, dimension (N)
    !>          On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are
    !>          the errors in the estimates of the corresponding elements in W.
    !>          On output, these errors are refined.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (2*N)
    !>          Workspace.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (2*N)
    !>          Workspace.
    !>

    PIVMIN

    !>          PIVMIN is DOUBLE PRECISION
    !>          The minimum pivot in the Sturm sequence for T.
    !>

    SPDIAM

    !>          SPDIAM is DOUBLE PRECISION
    !>          The spectral diameter of T.
    !>

    INFO

    !>          INFO is INTEGER
    !>          Error flag.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Beresford Parlett, University of California, Berkeley, USA
    Jim Demmel, University of California, Berkeley, USA
    Inderjit Dhillon, University of Texas, Austin, USA
    Osni Marques, LBNL/NERSC, USA
    Christof Voemel, University of California, Berkeley, USA

Definition at line 165 of file dlarrj.f.

  subroutine slarrj (integer n, real, dimension( * ) d, real, dimension( * ) e2, integer ifirst, integer ilast, real rtol, integer offset, real, dimension( * ) w, real, dimension( * ) werr, real, dimension( * ) work, integer, dimension( * ) iwork, real pivmin, real spdiam, integer info)

SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

Purpose:

    !>
    !> Given the initial eigenvalue approximations of T, SLARRJ
    !> does  bisection to refine the eigenvalues of T,
    !> W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial
    !> guesses for these eigenvalues are input in W, the corresponding estimate
    !> of the error in these guesses in WERR. During bisection, intervals
    !> [left, right] are maintained by storing their mid-points and
    !> semi-widths in the arrays W and WERR respectively.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix.
    !>

    D

    !>          D is REAL array, dimension (N)
    !>          The N diagonal elements of T.
    !>

    E2

    !>          E2 is REAL array, dimension (N-1)
    !>          The Squares of the (N-1) subdiagonal elements of T.
    !>

    IFIRST

    !>          IFIRST is INTEGER
    !>          The index of the first eigenvalue to be computed.
    !>

    ILAST

    !>          ILAST is INTEGER
    !>          The index of the last eigenvalue to be computed.
    !>

    RTOL

    !>          RTOL is REAL
    !>          Tolerance for the convergence of the bisection intervals.
    !>          An interval [LEFT,RIGHT] has converged if
    !>          RIGHT-LEFT < RTOL*MAX(|LEFT|,|RIGHT|).
    !>

    OFFSET

    !>          OFFSET is INTEGER
    !>          Offset for the arrays W and WERR, i.e., the IFIRST-OFFSET
    !>          through ILAST-OFFSET elements of these arrays are to be used.
    !>

    W

    !>          W is REAL array, dimension (N)
    !>          On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
    !>          estimates of the eigenvalues of L D L^T indexed IFIRST through
    !>          ILAST.
    !>          On output, these estimates are refined.
    !>

    WERR

    !>          WERR is REAL array, dimension (N)
    !>          On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are
    !>          the errors in the estimates of the corresponding elements in W.
    !>          On output, these errors are refined.
    !>

    WORK

    !>          WORK is REAL array, dimension (2*N)
    !>          Workspace.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (2*N)
    !>          Workspace.
    !>

    PIVMIN

    !>          PIVMIN is REAL
    !>          The minimum pivot in the Sturm sequence for T.
    !>

    SPDIAM

    !>          SPDIAM is REAL
    !>          The spectral diameter of T.
    !>

    INFO

    !>          INFO is INTEGER
    !>          Error flag.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Beresford Parlett, University of California, Berkeley, USA
    Jim Demmel, University of California, Berkeley, USA
    Inderjit Dhillon, University of Texas, Austin, USA
    Osni Marques, LBNL/NERSC, USA
    Christof Voemel, University of California, Berkeley, USA

Definition at line 165 of file slarrj.f.

Author

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